Question:medium

On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.

Updated On: Jan 20, 2026
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Solution and Explanation

1. Principal Quantum Number for 6th Period

For the 6th period, the principal quantum number is  n = 6  The orbitals that can participate in filling for this period are: \[ 6s,\; 4f,\; 5d,\; 6p \] (filled in this order according to the Aufbau principle and \((n + \ell)\) rule).

2. Number of Orbitals and Electrons

Each type of subshell has:

  • 6s: one orbital →  2 = { electrons} 
  • 4f: seven orbitals →  7* 2 = 14 { electrons} 
  • 5d: five orbitals → 2 = 10 \text{ electrons}
  • 6p: three orbitals →  3 * 2 = 6 \text{ electrons} 

Total electrons that can be successively added in these subshells: \[ 2 + 14 + 10 + 6 = 32 \text{ electrons} \]

3. Link to Number of Elements

Each new electron corresponds to a new element (new set of quantum numbers). Therefore, the number of elements in the 6th period equals the number of electrons that can be accommodated in \[ 6s,\; 4f,\; 5d,\; 6p \] i.e. \[ \boxed{32 \text{ elements}} \]

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